Some values were output from the database without being properly escaped. Most strings in question were sourced from the administrator panel.
All 1.5.x installs prior to and including 1.5.10 are affected.
Upgrade to latest Joomla! version (1.5.11 or newer).
A XSS vulnerability exists in the JA_Purity template which ships with Joomla! 1.5.
A XSS vulnerability exists in the user view of com_users in the administrator panel.